Download 2.3 Summary Critical areas summary

Critical Areas Kindergarten through Algebra II
1st Grade
(1) develop an understanding of
addition, subtraction, and strategies
for addition and subtraction within 20
(2) develop an understanding of
whole number relationships and place
value, including grouping in tens and
ones
(3) develop an understanding of linear
measurement and measuring lengths
as iterating length units
(4) reason about attributes of, and
compose and decompose geometric
shapes
2nd Grade
(1) extend understanding of base-ten
notation
(2) build fluency with addition and
subtraction
(3) use standard units of measure
(4) describe and analyze shapes
3rd Grade
(1) develop an understanding of
multiplication and division and
strategies for multiplication and
division within 100
(2) develop an understanding of
fractions, especially unit fractions
(fractions with numerator 1)
(3) develop an understanding of the
structure of rectangular arrays and of
area
(4) describe and analyze twodimensional shapes
4th Grade
(1) develop an understanding and
fluency with multi-digit
multiplication, and develop an
understanding of dividing to find
quotients involving multi-digit
dividends
(2) develop an understanding of
fraction equivalence, addition and
subtraction of fractions with like
denominators, and multiplication of
fractions by whole numbers
(3) understand that geometric figures
can be analyzed and classified based
on their properties, such as having
parallel sides, perpendicular sides,
particular angle measures, and
symmetry
5th Grade
(1) develop fluency with addition and
subtraction of fractions, and develop
an understanding of the
multiplication of fractions and of
division of fractions in limited cases
(unit fractions divided by whole
numbers and whole numbers divided
by unit fractions)
(2) extend division to 2-digit
divisors, integrate decimal fractions
into the place value system and
develop understanding of operations
with decimals to hundredths, and
develop fluency with whole number
and decimal operations
(3) develop an understanding of
volume
6th Grade
(1) connect ratio and rate to whole
number multiplication and division
and use concepts of ratio and rate to
solve problems
(2) complete understanding of
division of fractions and extend the
notion of number to the system of
rational numbers, which includes
negative numbers
(3) write, interpret, and use
expressions and equations
(4) develop an understanding of
statistical thinking
7th Grade
(1) develop an understanding of and
apply proportional relationships
(2) develop an understanding of
operations with rational numbers and
work with expressions and linear
equations
(3) solve problems involving scale
drawings and informal geometric
constructions, and work with two- and
three-dimensional shapes to solve
problems involving area, surface area,
and volume
(4) draw inferences about populations
based on samples
Geometry
(1) congruence, proof, and
constructions
(2) similarity, proof, and trigonometry
(3) extending to three dimensions
(4) connecting algebra and geometry
through coordinates
(5) circles with and without
coordinates
(6) applications of probability
8th Grade
(1) formulate and reason about
expressions and equations, including
modeling an association in bivariate
data with a linear equation, and
solving linear equations and systems
of linear equations
(2) grasp the concept of a function
and using functions to describe
quantitative relationships
(3) analyze two- and threedimensional space and figures using
distance, angle, similarity, and
congruence, and understand and
apply the Pythagorean Theorem
Algebra II
(1) polynomial, rational, and radical
relationships
(2) trigonometric functions
(3) modeling with functions
(4) connecting algebra and geometry
through inferences and conclusions
from data
Kindergarten
(1) represent, relating, and operating
on whole numbers, initially with sets
of objects
(2) describe shapes and space
More learning time in Kindergarten
should be devoted to number than to
other topics
Algebra I
(1) relationships between quantities
and reasoning with equations
(2) linear and exponential
relationships
(3) descriptive statistics
(4) expressions and equations
(5) quadratic functions and modeling
Critical Areas Kindergarten through Mathematics III
Kindergarten
(1) represent, relating, and operating
on whole numbers, initially with sets
of objects
(2) describe shapes and space.
More learning time in Kindergarten
should be devoted to number than to
other topics
3rd Grade
(1) develop an understanding of
multiplication and division and
strategies for multiplication and
division within 100
(2) develop an understanding of
fractions, especially unit fractions
(fractions with numerator 1)
(3) develop an understanding of the
structure of rectangular arrays and of
area
(4) describe and analyze twodimensional shapes
6th Grade
(1) connect ratio and rate to whole
number multiplication and division
and use concepts of ratio and rate to
solve problems
(2) complete understanding of
division of fractions and extend the
notion of number to the system of
rational numbers, which includes
negative numbers
(3) write, interpret, and use
expressions and equations
(4) develop an understanding of
statistical thinking
Mathematics I
(1) relationships between quantities
and reasoning with equations
(2) linear and exponential
relationships
(3) reasoning with equations
(4) descriptive statistics
(5) congruence, proof, and
constructions
1st Grade
(1) develop an understanding of
addition, subtraction, and strategies
for addition and subtraction within 20
(2) develop an understanding of
whole number relationships and place
value, including grouping in tens and
ones
(3) develop an understanding of linear
measurement and measuring lengths
as iterating length units
(4) reason about attributes of, and
compose and decompose geometric
shapes
2nd Grade
(1) extend understanding of base-ten
notation
(2) build fluency with addition and
subtraction
(3) use standard units of measure
(4) describe and analyze shapes
4th Grade
(1) develop an understanding and
fluency with multi-digit
multiplication, and develop an
understanding of dividing to find
quotients involving multi-digit
dividends
(2) develop an understanding of
fraction equivalence, addition and
subtraction of fractions with like
denominators, and multiplication of
fractions by whole numbers
(3) understand that geometric figures
can be analyzed and classified based
on their properties, such as having
parallel sides, perpendicular sides,
particular angle measures, and
symmetry
7th Grade
(1) develop an understanding of and
apply proportional relationships
(2) develop an understanding of
operations with rational numbers and
work with expressions and linear
equations
(3) solve problems involving scale
drawings and informal geometric
constructions, and work with two- and
three-dimensional shapes to solve
problems involving area, surface area,
and volume
(4) draw inferences about populations
based on samples
Mathematics II
(1) extending the number system
(2) quadratic functions and modeling
(3) expressions and equations
(4) applications of probability
(5) similarity, right triangle
trigonometry, and proof
(6) circles with and without
coordinates
5th Grade
(1) develop fluency with addition and
subtraction of fractions, and develop
an understanding of the
multiplication of fractions and of
division of fractions in limited cases
(unit fractions divided by whole
numbers and whole numbers divided
by unit fractions)
(2) extend division to 2-digit
divisors, integrate decimal fractions
into the place value system and
develop understanding of operations
with decimals to hundredths, and
develop fluency with whole number
and decimal operations
(3) develop an understanding of
volume
8th Grade
(1) formulate and reason about
expressions and equations, including
modeling an association in bivariate
data with a linear equation, and
solving linear equations and systems
of linear equations
(2) grasp the concept of a function
and using functions to describe
quantitative relationships
(3) analyze two-and threedimensional space and figures using
distance, angle, similarity, and
congruence, and understand and
apply the Pythagorean Theorem
Mathematics III
(1) inferences and conclusions from
data
(2) polynomial, rational, and radical
relationships
(3) missing measures of general
triangles
(4) radian measure
(4) trigonometric functions
(5) mathematical modelin
Critical Areas Kindergarten through Mathematics III